{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lecture 12 - Basics of Curve Fitting: Bayesian Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set_context('talk')\n",
    "sns.set_style('white')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Objectives\n",
    "\n",
    "+ Maximum Posterior Estimate\n",
    "+ Bayesian Linear Regression\n",
    "+ The evidence approximation\n",
    "+ Automatic relevance determination."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Readings\n",
    "\n",
    "+ These notes.\n",
    "+ [Ch. 3 of Bishop, 2006](http://www.amazon.com/Pattern-Recognition-Learning-Information-Statistics/dp/0387310738)\n",
    "+ [Mathematicalmonk, Bayesian Linear Regression](https://www.youtube.com/watch?v=dtkGq9tdYcI)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plese see the lecturee 9 before you start on this one.\n",
    "We just repeat some of the code that we developed there.\n",
    "In particular, we load the essential modules and we redefine the basis function classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Linear Basis\n",
    "class LinearBasis(object):\n",
    "    \"\"\"\n",
    "    Represents a 1D linear basis.\n",
    "    \"\"\"\n",
    "    def __init__(self):\n",
    "        self.num_basis = 2 # The number of basis functions\n",
    "    def __call__(self, x):\n",
    "        \"\"\"\n",
    "        ``x`` should be a 1D array.\n",
    "        \"\"\"\n",
    "        return [1., x[0]]\n",
    "    \n",
    "# We need a generic function that computes the design matrix\n",
    "def compute_design_matrix(X, phi):\n",
    "    \"\"\"\n",
    "    Arguments:\n",
    "    \n",
    "    X   -  The observed inputs (1D array)\n",
    "    phi -  The basis functions.\n",
    "    \"\"\"\n",
    "    num_observations = X.shape[0]\n",
    "    num_basis = phi.num_basis\n",
    "    Phi = np.ndarray((num_observations, num_basis))\n",
    "    for i in range(num_observations):\n",
    "        Phi[i, :] = phi(X[i, :])\n",
    "    return Phi\n",
    "\n",
    "\n",
    "# Here is a class for the polynomials:\n",
    "class PolynomialBasis(object):\n",
    "    \"\"\"\n",
    "    A set of linear basis functions.\n",
    "    \n",
    "    Arguments:\n",
    "    degree  -  The degree of the polynomial.\n",
    "    \"\"\"\n",
    "    def __init__(self, degree):\n",
    "        self.degree = degree\n",
    "        self.num_basis = degree + 1\n",
    "    def __call__(self, x):\n",
    "        return np.array([x[0] ** i for i in range(self.degree + 1)])\n",
    "    \n",
    "    \n",
    "class FourierBasis(object):\n",
    "    \"\"\"\n",
    "    A set of linear basis functions.\n",
    "    \n",
    "    Arguments:\n",
    "    num_terms  -  The number of Fourier terms.\n",
    "    L          -  The period of the function.\n",
    "    \"\"\"\n",
    "    def __init__(self, num_terms, L):\n",
    "        self.num_terms = num_terms\n",
    "        self.L = L\n",
    "        self.num_basis = 2 * num_terms\n",
    "    def __call__(self, x):\n",
    "        res = np.ndarray((self.num_basis,))\n",
    "        for i in range(num_terms):\n",
    "            res[2 * i] = np.cos(2 * i * np.pi / self.L * x[0])\n",
    "            res[2 * i + 1] = np.sin(2 * (i+1) * np.pi / self.L * x[0])\n",
    "        return res\n",
    "    \n",
    "\n",
    "class RadialBasisFunctions(object):\n",
    "    \"\"\"\n",
    "    A set of linear basis functions.\n",
    "    \n",
    "    Arguments:\n",
    "    X   -  The centers of the radial basis functions.\n",
    "    ell -  The assumed lengthscale.\n",
    "    \"\"\"\n",
    "    def __init__(self, X, ell):\n",
    "        self.X = X\n",
    "        self.ell = ell\n",
    "        self.num_basis = X.shape[0]\n",
    "    def __call__(self, x):\n",
    "        return np.exp(-.5 * (x - self.X) ** 2 / self.ell ** 2).flatten()\n",
    "    \n",
    "\n",
    "\n",
    "class StepFunctionBasis(object):\n",
    "    \"\"\"\n",
    "    A set of step functions.\n",
    "    \n",
    "    Arguments:\n",
    "    X   -  The centers of the step functions.\n",
    "    \"\"\"\n",
    "    def __init__(self, X):\n",
    "        self.X = X\n",
    "        self.num_basis = X.shape[0]\n",
    "    def __call__(self, x):\n",
    "        res = np.ones((self.num_basis, ))\n",
    "        res[x < self.X.flatten()] = 0.\n",
    "        return res"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use the motorcycle data set of lecture 7."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.loadtxt('motor.dat')\n",
    "X = data[:, 0][:, None]\n",
    "Y = data[:, 1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probabilistic Regression - Version 2\n",
    "+ We wish to model the data using some **fixed** basis/features:\n",
    "$$\n",
    "y(\\mathbf{x};\\mathbf{w}) = \\sum_{j=1}^{m} w_{j}\\phi_{j}(\\mathbf{x}) = \\mathbf{w^{T}\\boldsymbol{\\phi}(\\mathbf{x})\n",
    "}\n",
    "$$\n",
    "\n",
    "+ We *model the measurement process* using a **likelihood** function:\n",
    "$$\n",
    "\\mathbf{y}_{1:n} | \\mathbf{x}_{1:n}, \\mathbf{w}, \\sigma \\sim N(\\mathbf{w^{T}\\boldsymbol{\\phi}(\\mathbf{x})\n",
    "}, \\sigma^2).\n",
    "$$\n",
    "\n",
    "+ We *model the uncertainty in the model parameters* using a **prior**:\n",
    "$$\n",
    "\\mathbf{w} \\sim p(\\mathbf{w}).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian Prior on the Weights\n",
    "+ Consider the following **prior** on $\\mathbf{w}$:\n",
    "$$\n",
    "p(\\mathbf{w}|\\alpha) = \\mathcal{N}\\left(\\mathbf{w}|\\mathbf{0},\\alpha^{-1}\\mathbf{I}\\right) = \n",
    "\\left(\\frac{\\alpha}{2\\pi}\\right)^{\\frac{m}{2}}\\exp\\left\\{-\\frac{\\alpha}{2}\\lVert\\mathbf{w}\\rVert^2\\right\\}.\n",
    "$$\n",
    "+ We say:\n",
    "\n",
    "> Before we see the data, we beleive that $\\mathbf{w}$ must be around zero with a precision of $\\alpha$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Graphical Representation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n",
       " -->\n",
       "<!-- Title: bayes_regression Pages: 1 -->\n",
       "<svg width=\"206pt\" height=\"227pt\"\n",
       " viewBox=\"0.00 0.00 206.00 227.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 223)\">\n",
       "<title>bayes_regression</title>\n",
       "<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-223 202,-223 202,4 -4,4\"/>\n",
       "<g id=\"clust1\" class=\"cluster\">\n",
       "<title>cluster_0</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"64,-8 64,-155 134,-155 134,-8 64,-8\"/>\n",
       "<text text-anchor=\"middle\" x=\"99\" y=\"-15.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">j=1,...,n</text>\n",
       "</g>\n",
       "<!-- alpha -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>alpha</title>\n",
       "<ellipse fill=\"#d3d3d3\" stroke=\"#000000\" cx=\"27\" cy=\"-201\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"22.5\" y=\"-197.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">α</text>\n",
       "</g>\n",
       "<!-- w -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>w</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"27\" cy=\"-129\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"21.5\" y=\"-126.3\" font-family=\"Times,serif\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#000000\">w</text>\n",
       "</g>\n",
       "<!-- alpha&#45;&gt;w -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>alpha&#45;&gt;w</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M27,-182.8314C27,-175.131 27,-165.9743 27,-157.4166\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"30.5001,-157.4132 27,-147.4133 23.5001,-157.4133 30.5001,-157.4132\"/>\n",
       "</g>\n",
       "<!-- yj -->\n",
       "<g id=\"node5\" class=\"node\">\n",
       "<title>yj</title>\n",
       "<ellipse fill=\"#d3d3d3\" stroke=\"#000000\" cx=\"99\" cy=\"-57\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"93\" y=\"-54.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">y</text>\n",
       "<text text-anchor=\"start\" x=\"101\" y=\"-54.3\" font-family=\"Times,serif\" baseline-shift=\"sub\" font-size=\"14.00\" fill=\"#000000\">j</text>\n",
       "</g>\n",
       "<!-- w&#45;&gt;yj -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>w&#45;&gt;yj</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M42.2693,-113.7307C52.197,-103.803 65.3153,-90.6847 76.4363,-79.5637\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"79.1564,-81.7933 83.7527,-72.2473 74.2067,-76.8436 79.1564,-81.7933\"/>\n",
       "</g>\n",
       "<!-- sigma -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>sigma</title>\n",
       "<ellipse fill=\"#d3d3d3\" stroke=\"#000000\" cx=\"171\" cy=\"-129\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"167\" y=\"-125.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">σ</text>\n",
       "</g>\n",
       "<!-- sigma&#45;&gt;yj -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>sigma&#45;&gt;yj</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M155.7307,-113.7307C145.803,-103.803 132.6847,-90.6847 121.5637,-79.5637\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"123.7933,-76.8436 114.2473,-72.2473 118.8436,-81.7933 123.7933,-76.8436\"/>\n",
       "</g>\n",
       "<!-- xj -->\n",
       "<g id=\"node4\" class=\"node\">\n",
       "<title>xj</title>\n",
       "<ellipse fill=\"#d3d3d3\" stroke=\"#000000\" cx=\"99\" cy=\"-129\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"93\" y=\"-126.3\" font-family=\"Times,serif\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#000000\">x</text>\n",
       "<text text-anchor=\"start\" x=\"101\" y=\"-126.3\" font-family=\"Times,serif\" baseline-shift=\"sub\" font-size=\"14.00\" fill=\"#000000\">j</text>\n",
       "</g>\n",
       "<!-- xj&#45;&gt;yj -->\n",
       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>xj&#45;&gt;yj</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M99,-110.8314C99,-103.131 99,-93.9743 99,-85.4166\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"102.5001,-85.4132 99,-75.4133 95.5001,-85.4133 102.5001,-85.4132\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.dot.Digraph at 0x1a1ed7f810>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from graphviz import Digraph\n",
    "g = Digraph('bayes_regression')\n",
    "g.node('alpha', label='<&alpha;>', style='filled')\n",
    "g.node('w', label='<<b>w</b>>')\n",
    "g.node('sigma', label='<&sigma;>', style='filled')\n",
    "with g.subgraph(name='cluster_0') as sg:\n",
    "    sg.node('xj', label='<<b>x</b><sub>j</sub>>', style='filled')\n",
    "    sg.node('yj', label='<y<sub>j</sub>>', style='filled')\n",
    "    sg.attr(label='j=1,...,n')\n",
    "    sg.attr(labelloc='b')\n",
    "g.edge('alpha', 'w')\n",
    "g.edge('sigma', 'yj')\n",
    "g.edge('w', 'yj')\n",
    "g.edge('xj', 'yj')\n",
    "g.render('bayes_regression', format='png')\n",
    "g"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Posterior of the Weights\n",
    "+ Combining the likelihood and the prior, we get using Bayes rule:\n",
    "$$\n",
    "p(\\mathbf{w}|\\mathbf{x}_{1:n},\\mathbf{y}_{1:n}, \\sigma,\\alpha) = \n",
    "\\frac{p(\\mathbf{y}_{1:n}|\\mathbf{x}_{1:n}, \\mathbf{w}, \\sigma)p(\\mathbf{w}|\\alpha)}\n",
    "{\\int p(\\mathbf{y}_{1:n}|\\mathbf{x}_{1:n}, \\mathbf{w}', \\sigma)p(\\mathbf{w}'|\\alpha)d\\mathbf{w}'}.\n",
    "$$\n",
    "+ We say\n",
    "> The posterior summarizes our state of knowledge about $\\mathbf{w}$ after we see the data,\n",
    "if we know $\\alpha$ and $\\sigma$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Maximum Posterior Estimate\n",
    "+ We can find a point estimate of $\\mathbf{w}$ by solving:\n",
    "$$\n",
    "\\mathbf{w}_{\\mbox{MPE}} = \\arg\\max_{\\mathbf{w}} p(\\mathbf{y}_{1:n}|\\mathbf{x}_{1:n}, \\mathbf{w}, \\sigma)p(\\mathbf{w}|\\alpha).\n",
    "$$\n",
    "+ For Gaussian likelihood and weights:\n",
    "$$\n",
    "\\log p(\\mathbf{w}|\\mathbf{x}_{1:n},\\mathbf{y}_{1:n}, \\sigma,\\alpha) = \n",
    "- \\frac{1}{2\\sigma^2}\\lVert\\mathbf{\\Phi}\\mathbf{w}-\\mathbf{y}_{1:n}\\rVert^2 -\\frac{\\alpha}{2}\\lVert\\mathbf{w}\\rVert^2.\n",
    "$$\n",
    "+ With maximum:\n",
    "$$\n",
    "\\mathbf{w}_{\\mbox{MPE}} = \\left(\\sigma^{-2}\\mathbf{\\Phi}^T\\mathbf{\\Phi}+\\alpha\\mathbf{I}\\right)^{-1}\\mathbf{\\Phi}^T\\mathbf{y}_{1:n}.\n",
    "$$\n",
    "+ But, no analytic formula for $\\sigma$..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Stable Way to Compute the MAP Estimate\n",
    "+ Construct the positive-definite matrix:\n",
    "$$\n",
    "\\mathbf{A} = \\left(\\sigma^{-2}\\mathbf{\\Phi}^T\\mathbf{\\Phi}+\\alpha\\mathbf{I}\\right)\n",
    "$$\n",
    "+ Compute the [Cholesky decomposition](https://en.wikipedia.org/wiki/Cholesky_decomposition) of $\\mathbf{A}$:\n",
    "$$\n",
    "\\mathbf{A} = \\mathbf{L}\\mathbf{L}^T,\n",
    "$$\n",
    "where $\\mathbf{L}$ is lower triangular.\n",
    "+ Then, solve the system:\n",
    "$$\n",
    "\\mathbf{L}\\mathbf{L}^T\\mathbf{w} = \\mathbf{\\Phi}^T\\mathbf{y}_{1:n},\n",
    "$$\n",
    "doing a forward and a backward substitution.\n",
    "+ [scipy.linalg.cho_factor](http://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.linalg.cho_factor.html#scipy.linalg.cho_factor) and [scipy.linalg.cho_solve](http://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.linalg.cho_solve.html) can be used for this."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Radial Basis Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w_MPE:\n",
      "[  -0.34092858   -1.68904678   -3.19193641   -5.32186481  -18.32277585\n",
      " -100.03625967 -216.35332988 -241.24155683 -165.12418937  -26.36065749\n",
      "   51.58925071   52.3753626    17.89682441    9.91868847    9.65346397\n",
      "   -3.58400667   -3.22118958   -2.04465552    0.77592555    0.97107365]\n"
     ]
    }
   ],
   "source": [
    "import scipy.linalg\n",
    "ell = 2.\n",
    "alpha = 5\n",
    "sigma = 20.28\n",
    "Xc = np.linspace(0, 60, 20)\n",
    "phi = RadialBasisFunctions(Xc, ell)\n",
    "Phi = compute_design_matrix(X, phi)\n",
    "A = np.dot(Phi.T, Phi) / sigma ** 2. + alpha * np.eye(Phi.shape[1])\n",
    "L = scipy.linalg.cho_factor(A)\n",
    "w_MPE = scipy.linalg.cho_solve(L, np.dot(Phi.T, Y))\n",
    "print('w_MPE:')\n",
    "print(w_MPE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's predict on these points:\n",
    "X_p = np.linspace(0, 60, 100)[:, None]\n",
    "Phi_p = compute_design_matrix(X_p, phi)\n",
    "Y_p = np.dot(Phi_p, w_MPE)\n",
    "Y_l = Y_p - 2. * sigma # Lower predictive bound\n",
    "Y_u = Y_p + 2. * sigma # Upper predictive bound\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(X, Y, 'x', markeredgewidth=2, label='Observations')\n",
    "ax.plot(X_p, Y_p, label='MPE Prediction (Radial Basis Functions, alpha=%1.2f)' % alpha)\n",
    "ax.fill_between(X_p.flatten(), Y_l, Y_u, color=sns.color_palette()[1], alpha=0.25)\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$')\n",
    "plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Questions\n",
    "\n",
    "+ Experiment with different alphas.\n",
    "+ When are we underfitting?\n",
    "+ When are we overfitting?\n",
    "+ Which one (if any) gives you the best fit?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Issues with Maximum Posterior Estimate\n",
    "+ How many basis functions should I use?\n",
    "+ Which basis functions should I use?\n",
    "+ How do I pick the parameters of the basis functions, e.g., the lengthscale $\\ell$ of the RBFs, $\\alpha$, etc.?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probabilistic Regression - Version 3 - Bayesian Linear Regression\n",
    "+ For Gaussian likelihood and weights, the posterior is Gaussian:\n",
    "$$\n",
    "p(\\mathbf{w}|\\mathbf{x}_{1:n},\\mathbf{y}_{1:n}, \\sigma, \\alpha) = \\mathcal{N}\\left(\\mathbf{w}|\\mathbf{m}, \\mathbf{S}\\right),\n",
    "$$\n",
    "where\n",
    "$$\n",
    "\\mathbf{S} = \\left(\\sigma^{-2}\\mathbf{\\Phi}^T\\mathbf{\\Phi}+\\alpha\\mathbf{I}\\right)^{-1},\n",
    "$$\n",
    "and\n",
    "$$\n",
    "\\mathbf{m} = \\sigma^{-2}\\mathbf{S}\\Phi^T\\mathbf{y}_{1:n}.\n",
    "$$\n",
    "+ In general: [Markov Chain Monte Carlo](https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Posterior Predictive Distribution\n",
    "+ Using probability theory, we ask: What do we know about $y$ at a new $\\mathbf{x}$ after seeing the data.\n",
    "+ We have using the sum rule:\n",
    "$$\n",
    "p(y|\\mathbf{x}, \\mathbf{x}_{1:n}, \\mathbf{y}_{1:n}, \\sigma, \\alpha) = \n",
    "\\int p(y | \\mathbf{x}, \\mathbf{w}, \\sigma) p(\\mathbf{w}|\\mathbf{x}_{1:n}, \\mathbf{y}_{1:n},\\sigma,\\alpha)d\\mathbf{w}.\n",
    "$$\n",
    "+ For Gaussian likelihood and prior:\n",
    "$$\n",
    "p(y|\\mathbf{x}, \\mathbf{x}_{1:n}, \\mathbf{y}_{1:n}, \\sigma, \\alpha) = \\mathcal{N}\\left(y|m(\\mathbf{x}), s^2(\\mathbf{x})\\right),\n",
    "$$\n",
    "where\n",
    "$$\n",
    "m(\\mathbf{x}) = \\mathbf{m}^T\\boldsymbol{\\phi}(\\mathbf{x})\\;\\mbox{and}\\;s(\\mathbf{x}) = \\boldsymbol{\\phi}(\\mathbf{x})^T\\mathbf{S}\\boldsymbol{\\phi}(\\mathbf{x}) + \\sigma^2.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predictive Uncertainty\n",
    "+ The **predictive uncertainty** is:\n",
    "$$\n",
    "s^2(\\mathbf{x}) = \\boldsymbol{\\phi}(\\mathbf{x})^T\\mathbf{S}\\boldsymbol{\\phi}(\\mathbf{x}) + \\sigma^2.\n",
    "$$\n",
    "+ $\\sigma^2$ corresponds to the measurement noise.\n",
    "+ $\\boldsymbol{\\phi}(\\mathbf{x})^T\\mathbf{S}\\boldsymbol{\\phi}(\\mathbf{x})$ is the epistemic uncertainty induced by limited data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.linalg\n",
    "ell = 2.\n",
    "alpha = 0.001\n",
    "sigma = 20.28\n",
    "Xc = np.linspace(0, 60, 20)\n",
    "phi = RadialBasisFunctions(Xc, ell)\n",
    "Phi = compute_design_matrix(X, phi)\n",
    "A = np.dot(Phi.T, Phi) / sigma ** 2. + alpha * np.eye(Phi.shape[1])\n",
    "L = scipy.linalg.cho_factor(A)\n",
    "m = scipy.linalg.cho_solve(L, np.dot(Phi.T, Y) / sigma ** 2)  # The posterior mean of w\n",
    "S = scipy.linalg.cho_solve(L, np.eye(Phi.shape[1]))           # The posterior covariance of w\n",
    "Phi_p = compute_design_matrix(X_p, phi)\n",
    "Y_p = np.dot(Phi_p, m) # The mean prediction\n",
    "V_p_ep = np.einsum('ij,jk,ik->i', Phi_p, S, Phi_p) # The epistemic uncertainty\n",
    "S_p_ep = np.sqrt(V_p_ep)\n",
    "V_p = V_p_ep + sigma ** 2 # Full uncertainty\n",
    "S_p = np.sqrt(V_p)\n",
    "Y_l_ep = Y_p - 2. * S_p_ep  # Lower epistemic predictive bound\n",
    "Y_u_ep = Y_p + 2. * S_p_ep  # Upper epistemic predictive bound\n",
    "Y_l = Y_p - 2. * S_p # Lower predictive bound\n",
    "Y_u = Y_p + 2. * S_p # Upper predictive bound"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(X, Y, 'x', markeredgewidth=2, label='Observations')\n",
    "ax.plot(X_p, Y_p, label='Bayesian Prediction (Radial Basis Functions, alpha=%1.2f)' % alpha)\n",
    "ax.fill_between(X_p.flatten(), Y_l_ep, Y_u_ep, color=sns.color_palette()[2], alpha=0.25)\n",
    "ax.fill_between(X_p.flatten(), Y_l, Y_l_ep, color=sns.color_palette()[1], alpha=0.25)\n",
    "ax.fill_between(X_p.flatten(), Y_u_ep, Y_u, color=sns.color_palette()[1], alpha=0.25)\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$')\n",
    "plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sampling Posterior Models\n",
    "+ We can actually sample models (functions) from the posterior. Here is how:\n",
    "    + Sample a $\\mathbf{w}$ from $p(\\mathbf{w}|\\mathbf{x}_{1:n},\\mathbf{y}_{1:n}, \\sigma, \\alpha)$.\n",
    "    + Look at the sampled model:\n",
    "    $$\n",
    "    y(\\mathbf{x};\\mathbf{w}) = \\mathbf{w}^T\\boldsymbol{\\phi}(\\mathbf{x}).\n",
    "    $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$y$')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We have m, S, X_p, and Phi_p from before\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(X, Y, 'x', markeredgewidth=2, label='Observations')\n",
    "for i in range(10):\n",
    "    w = np.random.multivariate_normal(m, S)\n",
    "    Y_p_s = np.dot(Phi_p, w)\n",
    "    ax.plot(X_p, Y_p_s, color=sns.color_palette()[2], linewidth=0.5);\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Issues with Bayesian Linear Regression\n",
    "+ How many basis functions should I use?\n",
    "+ Which basis functions should I use?\n",
    "+ How do I pick the parameters of the basis functions, e.g., the lengthscale $\\ell$ of the RBFs, $\\alpha$, etc.?+"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Questions\n",
    "\n",
    "+ Experiment with different alphas, ells, and sigmas.\n",
    "+ When are we underfitting?\n",
    "+ When are we overfitting?\n",
    "+ Which one (if any) gives you the best fit?\n",
    "+ In the figure, right above: Increase the number of posterior $\\mathbf{w}$ samples to get a sense of the epistemic uncertainty induced by the limited data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probabilistic Regression - Version 4 - Hierarchical Priors\n",
    "+ So, how do we find all the parameters like $\\sigma$, $\\alpha$, $\\ell$, etc?\n",
    "+ These are all called **hyper-parameters** of the model.\n",
    "+ Call all of them\n",
    "$$\n",
    "\\boldsymbol{\\theta} = \\{\\sigma, \\alpha, \\ell,\\dots\\}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hierarchical Priors\n",
    "+ Model:\n",
    "$$\n",
    "y(\\mathbf{x};\\mathbf{w}) = \\sum_{j=1}^{m} w_{j}\\phi_{j}(\\mathbf{x}) = \\mathbf{w^{T}\\boldsymbol{\\phi}(\\mathbf{x})}\n",
    "$$\n",
    "+ Likelihood:\n",
    "$$\n",
    "\\mathbf{y}_{1:n} | \\mathbf{x}_{1:n}, \\mathbf{w}, \\boldsymbol{\\theta} \\sim p(\\mathbf{y}_{1:n}|\\mathbf{x}_{1:n}, \\mathbf{w}, \\boldsymbol{\\theta}).\n",
    "$$\n",
    "+ Weight prior:\n",
    "$$\n",
    "\\mathbf{w} | \\boldsymbol{\\theta} \\sim p(\\mathbf{w}| \\boldsymbol{\\theta}).\n",
    "$$\n",
    "+ Hyper-prior:\n",
    "$$\n",
    "\\boldsymbol{\\theta} \\sim p(\\boldsymbol{\\theta}).\n",
    "$$\n",
    "\n",
    "Graphically:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n",
       " -->\n",
       "<!-- Title: full_bayes_regression_2 Pages: 1 -->\n",
       "<svg width=\"206pt\" height=\"227pt\"\n",
       " viewBox=\"0.00 0.00 206.00 227.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 223)\">\n",
       "<title>full_bayes_regression_2</title>\n",
       "<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-223 202,-223 202,4 -4,4\"/>\n",
       "<g id=\"clust1\" class=\"cluster\">\n",
       "<title>cluster_0</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"64,-8 64,-155 134,-155 134,-8 64,-8\"/>\n",
       "<text text-anchor=\"middle\" x=\"99\" y=\"-15.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">j=1,...,n</text>\n",
       "</g>\n",
       "<!-- alpha -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>alpha</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"27\" cy=\"-201\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"22.5\" y=\"-197.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">α</text>\n",
       "</g>\n",
       "<!-- w -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>w</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"27\" cy=\"-129\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"21.5\" y=\"-126.3\" font-family=\"Times,serif\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#000000\">w</text>\n",
       "</g>\n",
       "<!-- alpha&#45;&gt;w -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>alpha&#45;&gt;w</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M27,-182.8314C27,-175.131 27,-165.9743 27,-157.4166\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"30.5001,-157.4132 27,-147.4133 23.5001,-157.4133 30.5001,-157.4132\"/>\n",
       "</g>\n",
       "<!-- yj -->\n",
       "<g id=\"node5\" class=\"node\">\n",
       "<title>yj</title>\n",
       "<ellipse fill=\"#d3d3d3\" stroke=\"#000000\" cx=\"99\" cy=\"-57\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"93\" y=\"-54.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">y</text>\n",
       "<text text-anchor=\"start\" x=\"101\" y=\"-54.3\" font-family=\"Times,serif\" baseline-shift=\"sub\" font-size=\"14.00\" fill=\"#000000\">j</text>\n",
       "</g>\n",
       "<!-- w&#45;&gt;yj -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>w&#45;&gt;yj</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M42.2693,-113.7307C52.197,-103.803 65.3153,-90.6847 76.4363,-79.5637\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"79.1564,-81.7933 83.7527,-72.2473 74.2067,-76.8436 79.1564,-81.7933\"/>\n",
       "</g>\n",
       "<!-- sigma -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>sigma</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"171\" cy=\"-129\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"167\" y=\"-125.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">σ</text>\n",
       "</g>\n",
       "<!-- sigma&#45;&gt;yj -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>sigma&#45;&gt;yj</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M155.7307,-113.7307C145.803,-103.803 132.6847,-90.6847 121.5637,-79.5637\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"123.7933,-76.8436 114.2473,-72.2473 118.8436,-81.7933 123.7933,-76.8436\"/>\n",
       "</g>\n",
       "<!-- xj -->\n",
       "<g id=\"node4\" class=\"node\">\n",
       "<title>xj</title>\n",
       "<ellipse fill=\"#d3d3d3\" stroke=\"#000000\" cx=\"99\" cy=\"-129\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"93\" y=\"-126.3\" font-family=\"Times,serif\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#000000\">x</text>\n",
       "<text text-anchor=\"start\" x=\"101\" y=\"-126.3\" font-family=\"Times,serif\" baseline-shift=\"sub\" font-size=\"14.00\" fill=\"#000000\">j</text>\n",
       "</g>\n",
       "<!-- xj&#45;&gt;yj -->\n",
       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>xj&#45;&gt;yj</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M99,-110.8314C99,-103.131 99,-93.9743 99,-85.4166\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"102.5001,-85.4132 99,-75.4133 95.5001,-85.4133 102.5001,-85.4132\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.dot.Digraph at 0x1a1ed8efd0>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g2 = Digraph('full_bayes_regression_2')\n",
    "g2.node('alpha', label='<&alpha;>')\n",
    "g2.node('w', label='<<b>w</b>>')\n",
    "g2.node('sigma', label='<&sigma;>')\n",
    "with g2.subgraph(name='cluster_0') as sg:\n",
    "    sg.node('xj', label='<<b>x</b><sub>j</sub>>', style='filled')\n",
    "    sg.node('yj', label='<y<sub>j</sub>>', style='filled')\n",
    "    sg.attr(label='j=1,...,n')\n",
    "    sg.attr(labelloc='b')\n",
    "g2.edge('alpha', 'w')\n",
    "g2.edge('sigma', 'yj')\n",
    "g2.edge('w', 'yj')\n",
    "g2.edge('xj', 'yj')\n",
    "g2.render('full_bayes_regression_2', format='png')\n",
    "g2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fully Bayesian Solution\n",
    "+ Just write down the posterior of everything:\n",
    "$$\n",
    "p(\\mathbf{w}, \\boldsymbol{\\theta}|\\mathbf{x}_{1:n}, \\mathbf{y}_{1:n}) \\propto p(\\mathbf{y}_{1:n}|\\mathbf{x}_{1:n}|\\mathbf{w},\\boldsymbol{\\theta})p(\\mathbf{w}|\\boldsymbol{\\theta})p(\\boldsymbol{\\theta}).\n",
    "$$\n",
    "+ and, somehow, sample from it..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Evidence Approximation\n",
    "+ Look at the marginal posterior of $\\boldsymbol{\\theta}$:\n",
    "$$\n",
    "p(\\boldsymbol{\\theta}|\\mathbf{x}_{1:n}, \\mathbf{y}_{1:n}) \\propto \n",
    "\\int p(\\mathbf{y}_{1:n}|\\mathbf{x}_{1:n}|\\mathbf{w},\\boldsymbol{\\theta})p(\\mathbf{w}|\\boldsymbol{\\theta})p(\\boldsymbol{\\theta})d\\mathbf{w}.\n",
    "$$\n",
    "\n",
    "+ Assume that the hyper-prior is relatively flat:\n",
    "$$\n",
    "p(\\boldsymbol{\\theta}) \\propto 1,\n",
    "$$\n",
    "\n",
    "+ Use a MAP estimate for $\\boldsymbol{\\theta}$:\n",
    "$$\n",
    "\\boldsymbol{\\theta}_{\\mbox{EV}} = \\arg\\max_{\\boldsymbol{\\theta}}\\int p(\\mathbf{y}_{1:n}|\\mathbf{x}_{1:n}|\\mathbf{w},\\boldsymbol{\\theta})p(\\mathbf{w}|\\boldsymbol{\\theta})d\\mathbf{w}.\n",
    "$$\n",
    "\n",
    "+ Analytical for Gaussian likelihood and prior."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation Evidence Approximation\n",
    "+ There is a fast algorithm for the evidence approximation for Bayesian linear regression.\n",
    "+ It would take about an hour to go over it. See Ch. 3 of (Bishop, 2006).\n",
    "+ We will use the implementation found in [scikit-learn](http://scikit-learn.org).\n",
    "+ If you don't have it:\n",
    "```\n",
    "conda install scikit-learn\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Radial Basis Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "best sigma: 22.206781585095047\n",
      "best alpha: 0.0024908742921719434\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import BayesianRidge\n",
    "ell = 2.\n",
    "Xc = np.linspace(0, 60, 50)\n",
    "phi = RadialBasisFunctions(Xc, ell)\n",
    "Phi = compute_design_matrix(X, phi)\n",
    "regressor = BayesianRidge()\n",
    "regressor.fit(Phi, Y)\n",
    "# They are using different names:\n",
    "sigma = np.sqrt(1. / regressor.alpha_)\n",
    "print('best sigma:', sigma)\n",
    "alpha = regressor.lambda_\n",
    "print('best alpha:', alpha)\n",
    "A = np.dot(Phi.T, Phi) / sigma ** 2. + alpha * np.eye(Phi.shape[1])\n",
    "L = scipy.linalg.cho_factor(A)\n",
    "m = scipy.linalg.cho_solve(L, np.dot(Phi.T, Y) / sigma ** 2)  # The posterior mean of w\n",
    "S = scipy.linalg.cho_solve(L, np.eye(Phi.shape[1]))           # The posterior covariance of w\n",
    "Phi_p = compute_design_matrix(X_p, phi)\n",
    "Y_p = np.dot(Phi_p, m) # The mean prediction\n",
    "V_p_ep = np.einsum('ij,jk,ik->i', Phi_p, S, Phi_p) # The epistemic uncertainty\n",
    "S_p_ep = np.sqrt(V_p_ep)\n",
    "V_p = V_p_ep + sigma ** 2 # Full uncertainty\n",
    "S_p = np.sqrt(V_p)\n",
    "Y_l_ep = Y_p - 2. * S_p_ep  # Lower epistemic predictive bound\n",
    "Y_u_ep = Y_p + 2. * S_p_ep  # Upper epistemic predictive bound\n",
    "Y_l = Y_p - 2. * S_p # Lower predictive bound\n",
    "Y_u = Y_p + 2. * S_p # Upper predictive bound"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(X, Y, 'x', markeredgewidth=2, label='Observations')\n",
    "ax.plot(X_p, Y_p, label='Bayesian Prediction (Radial Basis Functions, alpha=%1.2f)' % alpha)\n",
    "ax.fill_between(X_p.flatten(), Y_l_ep, Y_u_ep, color=sns.color_palette()[2], alpha=0.25)\n",
    "ax.fill_between(X_p.flatten(), Y_l, Y_l_ep, color=sns.color_palette()[1], alpha=0.25)\n",
    "ax.fill_between(X_p.flatten(), Y_u_ep, Y_u, color=sns.color_palette()[1], alpha=0.25)\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$')\n",
    "plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Issues with Bayesian Linear Regression\n",
    "+ How many basis functions should I use?\n",
    "+ Which basis functions should I use?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Questions\n",
    "\n",
    "+ Try the evidence approximation with the Fourier basis.\n",
    "+ Try the evidence approximation with the Step function basis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probabilistic Regression - Version 5 - Automatic Relevance Determination\n",
    "+ Use a different precision $\\alpha_i$ for each weight:\n",
    "$$\n",
    "p(w_j | \\alpha_j) \\propto \\exp\\left\\{-\\alpha_jw_j^2\\right\\},\n",
    "$$\n",
    "+ so that:\n",
    "$$\n",
    "p(\\mathbf{w}|\\boldsymbol{\\alpha}) = \\prod_{j=1}^mp(w_j|\\alpha_j).\n",
    "$$\n",
    "\n",
    "Graphically:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n",
       " -->\n",
       "<!-- Title: full_bayes_regression_3 Pages: 1 -->\n",
       "<svg width=\"228pt\" height=\"246pt\"\n",
       " viewBox=\"0.00 0.00 228.00 246.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 242)\">\n",
       "<title>full_bayes_regression_3</title>\n",
       "<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-242 224,-242 224,4 -4,4\"/>\n",
       "<g id=\"clust1\" class=\"cluster\">\n",
       "<title>cluster_0</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"64,-8 64,-158 134,-158 134,-8 64,-8\"/>\n",
       "<text text-anchor=\"middle\" x=\"99\" y=\"-15.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">j=1,...,n</text>\n",
       "</g>\n",
       "<g id=\"clust2\" class=\"cluster\">\n",
       "<title>cluster_1</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"142,-83 142,-230 212,-230 212,-83 142,-83\"/>\n",
       "<text text-anchor=\"middle\" x=\"177\" y=\"-90.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">i=1,...,m</text>\n",
       "</g>\n",
       "<!-- sigma -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>sigma</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"27\" cy=\"-132\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"23\" y=\"-128.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">σ</text>\n",
       "</g>\n",
       "<!-- yj -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>yj</title>\n",
       "<ellipse fill=\"#d3d3d3\" stroke=\"#000000\" cx=\"99\" cy=\"-57\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"93\" y=\"-54.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">y</text>\n",
       "<text text-anchor=\"start\" x=\"101\" y=\"-54.3\" font-family=\"Times,serif\" baseline-shift=\"sub\" font-size=\"14.00\" fill=\"#000000\">j</text>\n",
       "</g>\n",
       "<!-- sigma&#45;&gt;yj -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>sigma&#45;&gt;yj</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M36.2455,-114.9098C42.1877,-104.8947 50.5499,-92.4058 60,-83 62.9018,-80.1118 66.1694,-77.3546 69.5469,-74.7884\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"71.8501,-77.4479 78.0233,-68.8374 67.8278,-71.7189 71.8501,-77.4479\"/>\n",
       "</g>\n",
       "<!-- xj -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>xj</title>\n",
       "<ellipse fill=\"#d3d3d3\" stroke=\"#000000\" cx=\"99\" cy=\"-132\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"93\" y=\"-129.3\" font-family=\"Times,serif\" font-weight=\"bold\" font-size=\"14.00\" fill=\"#000000\">x</text>\n",
       "<text text-anchor=\"start\" x=\"101\" y=\"-129.3\" font-family=\"Times,serif\" baseline-shift=\"sub\" font-size=\"14.00\" fill=\"#000000\">j</text>\n",
       "</g>\n",
       "<!-- xj&#45;&gt;yj -->\n",
       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>xj&#45;&gt;yj</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M99,-113.8446C99,-105.3401 99,-95.0076 99,-85.4964\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"102.5001,-85.2481 99,-75.2482 95.5001,-85.2482 102.5001,-85.2481\"/>\n",
       "</g>\n",
       "<!-- alphai -->\n",
       "<g id=\"node4\" class=\"node\">\n",
       "<title>alphai</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"177\" cy=\"-204\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"170.5\" y=\"-201.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">α</text>\n",
       "<text text-anchor=\"start\" x=\"179.5\" y=\"-201.3\" font-family=\"Times,serif\" baseline-shift=\"sub\" font-size=\"14.00\" fill=\"#000000\">i</text>\n",
       "</g>\n",
       "<!-- wi -->\n",
       "<g id=\"node5\" class=\"node\">\n",
       "<title>wi</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"177\" cy=\"-132\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"start\" x=\"169.5\" y=\"-129.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">w</text>\n",
       "<text text-anchor=\"start\" x=\"180.5\" y=\"-129.3\" font-family=\"Times,serif\" baseline-shift=\"sub\" font-size=\"14.00\" fill=\"#000000\">i</text>\n",
       "</g>\n",
       "<!-- alphai&#45;&gt;wi -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>alphai&#45;&gt;wi</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M177,-185.8314C177,-178.131 177,-168.9743 177,-160.4166\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"180.5001,-160.4132 177,-150.4133 173.5001,-160.4133 180.5001,-160.4132\"/>\n",
       "</g>\n",
       "<!-- wi&#45;&gt;yj -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>wi&#45;&gt;yj</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M165.8511,-115.4838C158.6053,-105.436 148.5666,-92.7119 138,-83 134.8995,-80.1503 131.4588,-77.3902 127.9422,-74.8001\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"129.9357,-71.9232 119.7233,-69.1023 125.9475,-77.6761 129.9357,-71.9232\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.dot.Digraph at 0x1a1ed8e990>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g3 = Digraph('full_bayes_regression_3')\n",
    "g3.node('sigma', label='<&sigma;>')\n",
    "with g3.subgraph(name='cluster_0') as sg:\n",
    "    sg.node('xj', label='<<b>x</b><sub>j</sub>>', style='filled')\n",
    "    sg.node('yj', label='<y<sub>j</sub>>', style='filled')\n",
    "    sg.attr(label='j=1,...,n')\n",
    "    sg.attr(labelloc='b')\n",
    "with g3.subgraph(name='cluster_1') as sg:\n",
    "    sg.node('alphai', label='<&alpha;<sub>i</sub>>')\n",
    "    sg.node('wi', label='<w<sub>i</sub>>')\n",
    "    sg.attr(label='i=1,...,m')\n",
    "    sg.attr(labelloc='b')\n",
    "\n",
    "g3.edge('alphai', 'wi')\n",
    "g3.edge('sigma', 'yj')\n",
    "g3.edge('wi', 'yj')\n",
    "g3.edge('xj', 'yj')\n",
    "g3.render('full_bayes_regression_3', format='png')\n",
    "g3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, we need advanced techniques to carry out full Bayesian inference.\n",
    "A quick way out is to maximize the **evidence** with respect to all the $\\alpha_j$'s."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Radial Basis Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "best sigma: 21.18027075064695\n",
      "best alpha: [2.41622694e+01 4.60393723e+01 6.32601940e+01 6.60248705e+01\n",
      " 6.07577537e+01 6.30419345e+01 6.87983839e+01 7.19885330e+01\n",
      " 7.47478678e+01 7.18452626e+01 6.67773828e+01 7.04574032e+01\n",
      " 7.24203099e+01 6.04550341e+01 3.55032689e+01 1.10968067e-03\n",
      " 1.73367476e-04 1.99589349e+01 2.04616910e+01 1.05969545e-04\n",
      " 1.86715292e-02 3.14937763e+00 3.87600506e+01 6.61116485e+01\n",
      " 6.07405331e+01 3.38580108e+01 1.66337169e-03 9.09294119e-04\n",
      " 2.65807248e+01 3.21594802e+01 2.33882525e+01 3.57257599e+01\n",
      " 5.45115686e+01 5.24922174e+01 2.87934486e+01 9.11413331e-03\n",
      " 3.73413978e+01 5.18181885e+01 5.04733546e+01 3.90117514e+01\n",
      " 3.50099821e+01 4.39235876e+01 4.94959003e+01 5.09197345e+01\n",
      " 5.16755294e+01 5.22603627e+01 4.72226269e+01 3.69312958e+01\n",
      " 2.53199918e+01 1.38991944e+01]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import ARDRegression\n",
    "ell = 2.\n",
    "Xc = np.linspace(0, 60, 50)\n",
    "phi = RadialBasisFunctions(Xc, ell)\n",
    "Phi = compute_design_matrix(X, phi)\n",
    "regressor = ARDRegression()\n",
    "regressor.fit(Phi, Y)\n",
    "# They are using different names:\n",
    "sigma = np.sqrt(1. / regressor.alpha_)\n",
    "print('best sigma:', sigma)\n",
    "alpha = regressor.lambda_\n",
    "print('best alpha:', alpha)\n",
    "A = np.dot(Phi.T, Phi) / sigma ** 2. + alpha * np.eye(Phi.shape[1])\n",
    "L = scipy.linalg.cho_factor(A)\n",
    "m = scipy.linalg.cho_solve(L, np.dot(Phi.T, Y) / sigma ** 2)  # The posterior mean of w\n",
    "S = scipy.linalg.cho_solve(L, np.eye(Phi.shape[1]))           # The posterior covariance of w\n",
    "Phi_p = compute_design_matrix(X_p, phi)\n",
    "Y_p = np.dot(Phi_p, m) # The mean prediction\n",
    "V_p_ep = np.einsum('ij,jk,ik->i', Phi_p, S, Phi_p) # The epistemic uncertainty\n",
    "S_p_ep = np.sqrt(V_p_ep)\n",
    "V_p = V_p_ep + sigma ** 2 # Full uncertainty\n",
    "S_p = np.sqrt(V_p)\n",
    "Y_l_ep = Y_p - 2. * S_p_ep  # Lower epistemic predictive bound\n",
    "Y_u_ep = Y_p + 2. * S_p_ep  # Upper epistemic predictive bound\n",
    "Y_l = Y_p - 2. * S_p # Lower predictive bound\n",
    "Y_u = Y_p + 2. * S_p # Upper predictive bound"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(X, Y, 'x', markeredgewidth=2, label='Observations')\n",
    "ax.plot(X_p, Y_p, label='Bayesian Prediction (Radial Basis Functions, ARD)')\n",
    "ax.fill_between(X_p.flatten(), Y_l_ep, Y_u_ep, color=sns.color_palette()[2], alpha=0.25)\n",
    "ax.fill_between(X_p.flatten(), Y_l, Y_l_ep, color=sns.color_palette()[1], alpha=0.25)\n",
    "ax.fill_between(X_p.flatten(), Y_u_ep, Y_u, color=sns.color_palette()[1], alpha=0.25)\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$')\n",
    "plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Issues with Automatic Relevance Determination\n",
    "+ What about the input-dependent (heteroscedastic) noise? We will address this in our Markov Chain Monte Carlo classes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Questions\n",
    "\n",
    "+ Try ARD with the Fourier basis.\n",
    "+ Try ARD with the Step function basis.\n",
    "+ Try ARD with a basis that consists both of Fourier and RBFs. Which one's survive?"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
